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A DFT Study toward the Mechanism ofChromium-Catalyzed Ethylene Trimerization

Werner J anse van Rensburg,*, C r on je G r ove , J an P . S te y nb er g ,K l a u s B . S t a r k , J oha n J . H uyser, an d P e tr us J . S t e ynb er g *,

Sasol Technology (Pty) Ltd, R& D Division, 1 Klasie Havenga Road, Sasolburg 9570,S o u th A fr i ca , S a so l Te ch n o l o g y UK , P u r d i e B u i l d i n g , No r th Ha u g h S t A n d r e ws, Fi fe ,

Scotl and, KY 16 9ST, and Accelr ys In c., 1042 K ress Str eet, H ouston, T exas 77020

Recei ved October 3, 2003

A theoretical study of a mechanism for ethylene trimerization, catalyzed by Cr-pyrrolylcomplexes, is proposed a nd invest iga ted w ith dens ity fun ctional th eory m ethods. The selectiveforma tion of 1-hexene is genera lly a ccepted to follow a meta llacycle mecha nism. A deta iledsp in st a t e a n a lysis fo r a ct ive spe cies in t h e me ch a n ism sh ows t h a t t h e t r ip let sp in st a t erepresents the ground spin st a te for all st a tionary points. C omplete Gibbs free energy (298.15

K) surfaces ar e ma pped for both 5- and -bonding modes of pyrrole, as well as a stripped-down C l anion model a nd a full ClAlMe3an ion model. From th e calculat ed results it is shownt h a t t h e p rop ose d me t a l la cycle me ch a n ism is e n erg e t ica l ly fa vora ble , w it h me t a l la cyclegrowth identified a s the ra te-determining step. In a ddit ion, it is demonstrat ed tha t differentbonding modes of pyrrole are preferred at different stages in the proposed mechanism,effectively suggesting tha t ring slippage of the pyrrole occurs on t he minimum energy pathon t h e p ot e n t ia l e n e rg y su rfa ce. F ro m t h e ca lcu la t e d re su lt s imp ort a n t in sig h t is g a in edinto the hemilabile nature of the pyrrole ring in th e mecha nism, wh ich in t urn sh eds lighton the general r equirements for a n effective ligand in Cr-cata lyzed ethylene trimerization.

Introduction

The tra nsi t ion metal cata lyzed oligomerizat ion ofethylene is tradi t ional ly used to synthesize R-olefinswith product mixtures usually consisting of a mixtureof even-numbered chain lengths (C 4-C 26).1 The impor-tance of R-olefins is rea lized from it s a pplica tion in t heproduction of linear low-density polyethylene (LLDP E,C 6and C 8), plasticizer and detergent alcohols (C 6-C 16),and synt het ic l ub ricant s . 2 Selective trimerizat ion ofethylene t o produce 1-hexene is highly desira ble beca useit would avoid the production of unwanted olefins thatconventional transition metal oligomerization processesproduce. A lot of current interest is focused on the

development of homogeneous catalyst systems to selec-tively trimerize ethylene. Cr-based catalysts are found

to be especially w ell suited for the s elective trimerizat ionof ethylene, as is evident from a number of l i teraturereports,3-6 although Ti,7 Ta,8 a n d V9 cat a l ysi s i s a l sofound t o have a pplicat ion in t his ar ea.

Whereas the mechanism for ethylene oligomerizationf ol low s t h e s t a n d a r d C os s ee-Arlman coordination/migratory insertion mechanism,10 the selective conver-sion of ethylene to essentia lly 1-hexene is at tribut ed to

* Corresponding authors. E-mail: Werner.J ansevanRensburg@sasol.

com; P etrie.Steyn berg@sas ol.com. Sa sol Technology (Pty ) Ltd. Sa sol Technology U K. Accelrys Inc.(1) For examples, see: (a) Skupinska, J .Chem. Rev.1991, 9 1, 613.

(b) Keim, W.; Kowa ldt, F. H.; G oddard, R.; Kru ger, C. Angew. Chem.,I n t . E d . E n g l . 1978, 1 7, 466. (c) Svejda, S . A.; Brookhar t, M. Or gano-metall ics1999, 18, 65. (d) Killian, C. M.; J ohnson, L. K.; Brookhart,M. Organometall ics1997, 1 6, 2005. (e) Mecking, S. Coord. Chem. Rev.2000, 203, 325. ( f) Ruther, T.; B raussa ud, N.; Cavel l , K. J . Organo-metall ics2001, 2 0, 1247. (g) Britovsek, G. J . P .; Mast roianni, S.; S olan ,G. A.; Baugh, S . P. D. ; Redshaw, C. ; Gibson, V. C. ; White, A. J . P. ;William s, D . J . ; Elsegood, M. R. J . C h e m . Eu r . J . 2000, 6, 2221.

(2) Vogt, D . In Appli ed H omogeneous Catalysis w ith Organometall icCompounds; Corni ls, B . , Herrma nn, W. A., Eds. ; VCH: Weinheim,Germany, 1996; p 245.

(3) (a) Many ik, R. M.; Walker, W. E.; Wilson, T. P . J . C a t a l . 1977,47, 197. (b) Yang, Y.; Kim, H.; Lee, J .; Paik, H.; J ang, H. G. Appl. Catal.A 2000, 1 93, 29. (c) Wassers cheid, P.; Gr imm, S .; Kohn , R.; H au fe, M.Ad v . Sy n t h . C a t a l . 2001, 3 43, 814. (d) Carter, A.; Cohen, S. A.; Cooley,N. A.; Murphy, A.; Scutt, J .; Wass, D . F. J . Chem. Soc., Chem. Comm un.2002, 858. (e) Monoi, T.; S as ak i, Y. J . M ol . C a t a l . A: C h em . 2002, 1 87,135. (f) McGu inness, D . S.; Wasserscheid, P .; Keim, W.; Hu, C .; En glert,

U.; Dixon, J . T.; G rove, C. J . Chem. Soc., Chem. Comm un. 2003, 334.(g) McGuinn ess, D. S .; Wasserscheid, P .; Keim, W.; Morgan, D.; D ixon,J . T.; Bollmann, A.; Maumela, H.; Hess, F.; Englert, U. J . Am . C h em .Soc.2003, 125, 5272. (h) Morga n, D . H.; S chwikkar d, S. L.; Dixon, J .T.; Nair, J . J .; Hunter, R. Adv. Synth. Catal. 2003, 939. (i) Commereuc,D. ; Drochon, S . ; Saussine, L . (Inst i tut F rancais du P etrole) US Pa tent6031145, 2000. (j) Wu, F .-J . (Amoco Corp.) U S P at ent 5811618, 1998.(k) Aoyama, T.; Mimura, H.; Yamamoto, T.; Oguri, M.; Koie, Y. (TosohCorp.) J P P at ent 09176229, 1997.

(4) Br iggs, J . R . J. Chem. Soc., Chem. Commun. 1989, 674.(5) (a) Reagan, W. K.; Pettijohn, T. M.; Freeman, J . W.; Benham,

E. A. (Phillips Petroleum Co.)US Patent 5786431, 1998. (b) Lashier,M. E . (Ph illips P etroleum Co.) EP 0780353A1, 1997.

(6) (a) J olly, P . W.Acc. Chem. Res. 1996, 29, 544. (b) Emrich, R.;Heinema nn, O.; J olly, P . W.; Kr uger, C.; Verhovnik, G. P . J .Or gano-metall ics1997, 16, 1511.

1207Organometall ics2004, 23 , 1207-1222

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metal lacycle intermediat es.4,6 Very recently proposedmetallacycle mechanisms for Ti-11 an d Ta-cata lyzed12

ethylene trimerization were investigated with high-leveldensity functional theory (DFT). To t he best of ourknowledge, however, no t heoretica l study of a possibleCr-cata lyzed mecha nism for ethylene trimerizat ion ha syet b een report ed. Thi s i s a t t r i but ed t o t he l ack ofavai lable fundamental experimental data on both theexact na tur e of Cr species in the ca ta lytic cycle a nd th eelectronic structure of Cr complexes w hich requirenotoriously challenging open sh ell calcula tions.

In the present paper we propose an d investigat e anethylene trimerizat ion mechan ism based on Cr-pyrrolylcomplexes, which represents one of the most successfulethylene trimerization systems known (Phillips Petro-leum Company).5 Experimental ly i t is found that the

combina tion of chromium t ri(ethylhexa noat e) [Cr(EH )3],dimethylpyrrole, t riethylaluminum, an d diethyla lumi-num chloride yields a highly reactive ethylene trimer-ization system.5 The proposed mechanism for ethylenetrimerizat ion with a pyrr ole-based syst em is illustra tedin Figure 1.4,6

Catalyst initiation is proposed to involve deprotona-tion of t he pyrrole l igand, one-electron inner shellreduction of the Cr(III) in Cr(EH)3, l igand exchange,ani on form at i on, and coordi nat i on of t w o et hylenemolecules to yield the neutral Cr(II) species, 1, a s t h efirst active intermediate in the catalytic cycle. Alkyla-luminum (TEA) a ctivat ion of th e Cr(III) cat a lyst precur-sor is believed to involve homolytic cleavage of a Cr-O

bond through interaction of Al with the carbonyl oxygenof a n ethylhexan oat e fragment, a s presented schemat i-cal ly in Figure 2. From this one-electron inner shell

reduction process an active Cr(II) species is generatedt oget her w i t h a correspondi ng et ha ne radi cal .13 Asimilar Cr(III) activation process involving interactionof Cr(EH)3with TEA, in the presence of an alternativeliga nd (2,6-dipheny lphenol/a nisole), is s uggest ed in av ery rec ent report b y Morgan et a l.3h I n t hei r w orkma gnetic susceptibility measur ements on the activat edcatalyst system showed eff values of 5.17 and 3.61 Bin xylene a nd t oluene, respectively, indica tive of Cr(II)species. This effectively supports the suggestion thatCr(II) intermediates account for the ini t ial act ivatedcata lytic species.

The a nion fragment of 1 is proposed to consist of a

ClAlEt 3 unit , or oligomer thereof,3b

w hi ch rem ai nscoordinat ed throughout the mecha nist ic cycle. Metal-lacycle forma tion from 1 involves oxida tive a ddition ofthe tw o ethylene fragments to yield a f ive-memberedCr(IV) metallacycle, 2. This is followed by t he coordina -tion of a third ethylene molecule to yield3. Subsequentmetallacycle growth results from insertion of the thirdethy lene molecule int o the five-membered met a llacyclicring to y ield the seven-membered met alla cycle species4. The precedence for five- and seven-membered Crmeta llacycles has been established by the isolat ion an dcharacterizat ion of crystal structures on related com-plexes.6,14 1-Hexene libera tion is a fforded by r eductiveeliminat ive intra molecular -hydrogen migra tion to the

-carbon and regeneration of the active catalytic Cr(II)species, 1, upon coordina tion of tw o ethylene molecules.

In t his th eoretical stud y high-level density functionaltheory is used to assess the val idi ty of the proposedmechanism (Figure 1). Although a number of assump-tions w ith regard to the mechan ism are ma de, e.g., thepresence of Cr(II) and Cr(IV) as act ive species in t hem echani sm a nd nat ure of t he ani oni c fragm ent , i t i sbel ieved that the proposed mechanism represents anacceptable hypothesis sui table as a thorough first at-tempt to theoretically investigate a Cr-catalyzed ethyl-ene trimerizat ion mechanism. In a ddit ion t o the ma p-p in g of t h e p ot e nt i a l e ne rg y s u rf a ce (P E S ) o f t h eproposed mechanism a number of additional fundamen-

ta l a spects a re a lso addressed, e.g., the preferred spinsta te of var ious Cr species, the influence of coordina tionm od e of t h e p yr r ol e l i ga n d , n a t u r e of t h e a n i on ic

(7) (a) D eckers, P. J . W.; H essen, B .; Teuben, J . H . Angew. Chem.,I n t . E d . 2001, 40, 2516. (b) Deckers, P . J . W.; Hessen, B.; Teuben, J .H . Organometall ics2002, 21, 5122. (c) Pellechia, C.; Pappalardo, D.;Ol iva, L . ; Ma zzeo, M.; G ruter, G .-J . M acromolecul es2000, 33, 2807.

(8) Andes, C.; Ha rkins, S. B .; Murtuza , S.; Oyler, K.; Sen, A.J . A m .Chem. Soc. 2001, 123, 7423.

(9) Santi , R.; Romano, A. M.; Grande, M.; Sommazzi, A.; Masi, F.;Pr oto, A. (ENI CH EM S.P .A.) WO 0168572, 2001.

(10) (a) Cossee, P. J . C a t a l . 1964, 3, 80. (b) Arlman , E . J . ; Cossee,P . J . C a t a l . 1964, 3, 99.

(11) (a) B lok, A. N. J . ; B udzelaa r, P . H . M.; G al, A. W. Organome-t a l l i c s 2003, 2 2, 2564. (b) de Bruin, T. J . M.; Mag na , L.; Ra yba ud, P .;Toulhout, H. Organometall ics2003, 22, 3404.

(12) Yu, Z.-X.; Houk, K. N. Angew. Chem., Int. Ed. 2003, 42, 808.

(13) From unpublished in-house experimental studies on the Cr-p y r r ol y l c a t a l y s t s y s t em t h e f ol low i n g ob s er v a t i on s a r e m a d e f orcatalyst ac t ivat ion: (i ) During TEA/Cr(EH)3 c a t a l y s t a c t iv a t i on ag a s e ou s w h i t e h a z e i s o bs e r ve d a s p a r t o f t h e r e a ct i on m i xt u r e .Al t h ou g h n ot a n a l y z e d a s s u ch , i t i s s t r o n g ly b el ie ve d t h a t t h i sobservation is explained by t he formation of butan e gas r esulting fromthe coordina tion of two ethan e rad ical species, which is in tur n formedduring the activation process. (ii) During activation a distinct colorchange from green to brown is observed, in l ine wi th a Cr(III) to Cr-(II) oxidat ion stat e chan ge.

(14) Bercaw, J . E. The 15th Interna t ional S ymposium on OlefinMetathesis and Related Chemistry (ISOM XV) J uly 28-Aug 1, 2003,Kyoto, J apan .

Figure 1. P r o pos ed m et a l la c y cle m ech a n is m f or C r -pyrrolyl-catalyzed trimerization of ethylene.

Figure 2. Proposed mechanism for Cr(III) activation byTE A.

1208 Or gan om et al l i cs, V ol . 23, N o. 6, 2004 J an se van R en sbu r g et al .


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fragment, conformations of the metallacycle rings, andcharge distribution effects.

Computational Details

For most equilibrium str uctures preliminary geometrieswere optimized by using the P M315 semiempirical Hamiltonianava ilable in Spa rta n02 (Wavefunction Inc.).16 This approache ns u r ed t h e r a p id s ca n n i n g o f t h e p r el im i n a r y P E S a n dprovided reasonable sta rt ing geometries for higher level DF Tcalculations. All final geometry optimizations were performedw i t h t h e D M o l3 density functiona l theory (DFT) code17 a simplemented in the Mat erialsSt udio (Version 2.1.5) programpackage of Accelrys Inc. The nonlocal generalized gradientapproximation (GGA) functional by Perdew and Wang (PW91)18

was used for all geometry optimizations. The convergencecriteria for these optimizations consisted of threshold valuesof 2 10-5 Ha , 0.00189 H a/, an d 0.00529 for energy,gradient, an d displacement convergence, respectively, w hilea self-consistent-field (SC F) density convergence thresholdvalue of 1 10-6 Ha was specified. DMol3 utilizes a basis setof numeric atomic functions, which a re exact solutions t o theKohn-Sham e q u at ions for t he a t oms. 19 These basis sets areg ene r al ly mor e c omp let e t han a compar a b le se t of l inear lyindependent Ga ussian functions and ha ve been demonstra ted

to have small basis set superposit ion errors.19 In the presentst u d y a p olar ize d sp lit vale nce b a sis se t , t e r med d ou b lenumeric polarized (DNP) basis set, h as been used. All geometryoptimizations employed highly efficient delocalized internalcoordinates. 20 The use of delocalized coordinates significantlyreduces the nu mber of geometry optimiza tion itera tions neededto optimize larger molecules compa red to the use of tra ditiona lCartesian coordinates.

All the geometries optimized were also subjected to fullf r eq u e ncy ana ly ses a t t he same GG A/P W91/D N P leve l oftheory to verify the nature of all stationary points. Equilibriumgeometries were characterized by the absence of imaginaryfr eq u e ncies . P r e liminar y t r ansit ion s t a t e g e ome t r ies we r eobtained by either th e DMol3 PE S scan functionality in C erius2

(Version 4.8, Accelrys, Inc.) or the integrated linear synchro-

nous tr a nsit /qua dra tic synchronous t ra nsit (LS T/QST) alg o-rithm 21 available in MaterialsStudio. These preliminary struc-tures were then subjected to full TS optimizations using aneigenvector following algorithm. For selected tr an sit ion sta tegeometries confirmation calculations, involving intrinsic reac-t ion p at h (I RP )22 calculations, were performed in which thepath connecting reagent, TS, and product are mapped. TheIRP calcula tions, performed a t th e sam e GG A/P W91/DNP levelof theory, ensured the direct connection of transit ion stateswith the respective reactan t a nd product geometries. All IRPcalculations performed a re referred to in the text. All tra nsitionstructure geometries exhibited only one imagina ry frequencyin th e reaction coordina te. All reported energies refer to G ibbsfree energy corrections to the total electronic energies at 298.15

K wit h the inclusion of zero-point energy (ZP E) corrections,unless explicit ly stated to the contrary.

A comprehensive a na lysis of preferred mult iplicity of Cr forselected C r(II) and Cr(IV) complexes, including representa tiveexamples for both equilibrium and transition state geometries,wa s p er for me d b y cond uc t ing ope n she ll c a lcu lat ions forelectrons in the excited states. For singlet structures closedshell optimizations were performed. The thr ee possible spinstates of Cr(II) complexes (singlet , tr iplet , and quintet) andtwo spin states for Cr(IV) complexes (singlet and triplet) were

consid e re d . F r om t his ana ly sis (d iscu ssed in d e t ai l in t heResults a nd D iscussion section) a preferred triplet spin sta tefor sta t ionary points in t he proposed mechanistic cycle (con-sist ing of only Cr(II) and Cr(IV) species) was established, inagreement wit h the tendency of Cr to exhibit high spin sta tes.Consequently, unrestricted triplet spin sta tes w ere specifiedfor all geometry optimizations unless explicit ly stated to thecontrary.

Self-consistent-field (SCF) convergence problems are fre-quent ly encount ered for open shell organometa llic systems. Toenhance SCF convergence efficiency during optimization ofstat ionary points, a small electron thermal smearing value of0.005 Ha was specified for all calculations unless explicit lys t a t e d t o t h e co nt r a r y . Th e t h e rm a l s m ea r i n g op t ion i nMat erialsSt udio makes use of a fractional electron occupancyscheme at the Fermi level according to a finite-temperatureFermi function.23,24 The ap p licat ion of t his t e chniq u e w asju st i f ie d b y t he r e la t ive ly s imilar e ner g y d iffer e nce s a ndgeometries obtained for reference calculat ions in w hich smear-ing and no smearing were used. Population analysis (Hirshfeldcharg es) wa s performed for G G A/P W91/DNP optimized st ruc-tures at the same level of theory. 25

Results and Discussion

Ligand Coordination Mode. Throughout this studypyrrole is used a s model ligan d for 2,5-dimethylpyrr olecommonly used in experimental studies.26 Py rrole cantheoretically coordinate in a number of ways to a metalcenter, including pentahapto (5) , t r i hapt o (3) , a n d

sigma () bonding (with a covalent Cr-

N interaction)m odes. I n t he 5- b ondi ng m ode t he l i gand ac t s as at r i dent at e l igand, cont r i but i ng s ix elect rons t o t hecoordinat ion sphere of Cr, w hile the -bonding mode ismonodentate, contributing only two electrons to thevalence shell. Therefore, species1 a nd 3 in Figure 1 a re16-electr on complexes for 5-pyrr ole a nd 12-electr oncomplexes for -pyrrole, whereas 2 a nd 4 in Figure 1are 14-electron complexes for 5-pyrrole and 10-electroncomplexes for -pyrrol e. I t i s t hus evi dent t hat t hebonding mode of pyrrole will dicta te t he va lence electr oncount in t he a ctive ca ta lytic species. For a ll complexesoptimized in this study the 5- and -bonding modes ofpyrrole, which represents the t wo most likely extremes

for bonding of pyrrole,27

were explicitly considered toa s s es s t h e p re fe rr ed l ig a n d b on d in g m od es of t h erelevant complexes.

(15) Stew ar t, J . J . P. J. Comput. Chem. 1989, 10, 209.(16) Wavefunction, I nc.: 18401 Von Ka rma n Avenue, S uite 370,Irvine, CA 92612.

(17) (a) Delley, B. J. Chem. Phys. 1990, 92, 508. (b) Delley, B. J .Phys. Chem.1996, 1 00, 6107. (c) Delley, B. J . Chem. Phys.2000, 1 13,7756.

(18) P erdew, J . P .; Wang, Y. Phys. Rev. 1992, B 45, 13244.(19) Delley, B. D en s i t y F u n c t i o n a l T h eor y : A T o ol f or C h em i s t r y ;

S e m in a r i o, J . M . , P o li t z er , P . , E d s . ; E l s ev ie r : Am s t e rd a m , Th eNetherlands, 1995.

(20) Andzelm, J .; King-Smith, R. D.; Fitzgerald, G. Chem. Phys. L ett.2001, 335, 321.

(21) Govind, N.; Petersen, M.; F i tzgerald, G . ; K ing-Smith, D. ;Andzelm, J . Comput. Mater. Sci. (accepted for publication).

(22) The IRP technique used in MaterialsStudio (Accelrys Inc . ,Version 2.1.5) also corresponds to the intui t ive minimum energypath wa y (MEP ) connecting two structures a nd is based on the nudged-elastic ban d (NEB ) algorithm of Henkelman a nd J onsson: Henkelman,G.; J onsson, H. J. Chem. Phys. 2000, 113, 9978.

(23) Delley, B. In M o d er n D en s i t y F u n c t i o n al T h eor y : A T o ol f or Chemistry; S e m in a r i o, J . M . , P o li t z er , P . , E d s . ; Th e or e t ic a l a n dComputat ional Chemistry, Vol. 2, E lsevier: Amsterdam, The Neth-erlands , 1995.

(24) Weinert, M.; Da venport, J . W. Phys. Rev. B 1992, 45, 13709.(25) (a) Hirshfeld, F. L. T h e o r . C h i m . Ac t a B 1977, 44, 129. (b)

Del ley, B . Chem. Phys. Lett. 1986, 11 0, 329.(26) It w as found from in-house experimenta l studies tha t ethy lene

trimerizatrition runs w ith pyrrole as ligand behave similarly comparedto 2,5-dimethylpyrrole.

(27) Reagan, W. K. Symposium on novel preparation and conversionof light olefins presented before the Division of Petroleum Chemist ry,Inc., American Chemical Society, Miami Beach meeting, Sept 10-15,1989.

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Multiplicity. Coordina tion compounds conta iningsoft -acidic ligands (e.g., Cp-, pyrrole-anions, etc.) areoften found in low oxidation states, where the stronglycovalent meta l-ligand interactions typically enforce the18-electron ru le an d a spin-paired ground sta te. C r(0),w i t h i t s 3d 54s 1 valence shell , as well as the di fferentoxi dat i on s t a t es of C r ( C r 1+-C r 5+), exhibit unpa iredelect rons i n t he v al ence shel l, and t he associ at edparam a gnet i sm m a kes N MR c hara ct eriz at i on of C r

complexes impractical. Organometallic complexes of thisnature, sometimes also referred to as metallaradicals,are notoriously difficult to accommodate computation-al ly due to SCF convergence problems often encoun-tered, as well as the computat ional ly expensive natureof open sh ell calcula tions. These phenomena a re prob-ably the reasons that theoretical studies based on Crchemistr y a re less frequent ly encountered compar ed toother transi t ion metals.

The relevance of electron pairing energy as a possibledestabi l iz ing factor for l igand coordination to Cr wasa ddressed in open shell computa tional st udies (MP 2 andDFT) by Cacelli et al.28 In th eir work it w a s pointed outtha t in th e presence of an addit ional P H 3donor, wh ich

will exert a favora ble chela te effect, 22.5 kcal/mol isneeded to promote the q ua rtet ground st at e 15-electroncomplex, CpCr (III)C l2(P H 3), to the doublet excited state(i.e. , vacating a singly occupied valence shell orbital),wh ile only 16.5 kcal/mol is ga ined upon forma tion of th edoublet 17-electron complex, CpC r (III)C l2(P H 3)2, from thedoublet 15-electron precursor, CpCr (III)C l2(P H 3). Thisshows tha t the energy ga ined upon donor l igand coor-di nat i on i s not suff ici ent t o ov ercom e t he elect ronpairing energy of the Cr(III) center. In more recentcalculations29 t he i m port anc e of spin s t a t e crossingduring the reaction of transi t ion metal compounds isemphasized. These spin crossing phenomena are alsoreferred to as two-state reactivi ty (TSR)30 involving

participation of spin inversion at transition states. Fromthese studies it is clear that consideration of all possiblespin states of a transi t ion metal center is essential toensure that when spin state crossing does occur, them i ni m um energy crossing poi nt (MEC P ) ha s b eenob t a in ed . M E C P s a r e p a r t icu la r l y i mp or t a n t w h e nequilibrium st ructures for r eagents a nd products havedifferent spin states and when transi t ion state geom-etries exhibit different spin sta tes, on the lowest energypat h, compar ed to reag ents a nd/or products. Obta iningexperimental evidence for spin sta te crossings w ouldrequire spin state measurements of intermediates, achallenging29 aspect tha t ha s not been conducted suc-cessfully yet. Therefore, spin state crossings are more

conveniently a ddressed by a computa tional a pproach.29,30From these studies i t was observed that the nature oft h e e xch a n g e p a r t of t h e D F T f u n ct i on a l s t r on g lyi nfl uences t he ac curac y of t he com put ed spi n s t a t esplitt ings, which is part icular ly strong for the first-rowtransi t ion metals (Sc-Cu) with presumably large ex-

chang e interactions between th e compact 3d orbita ls ofthese metals. Consequently, the identi ficat ion of the

ground spin states for the di fferent Cr(II) and Cr(IV)equilibrium a nd t ra nsition st at e geometries in our stud yis essential to ensure the location of the lowest energyst at i onary poi nt s on t he c al c ul at ed P ESs. C urrent l y ,methodology t o accura tely compute ME CP energies foropen shell transition metal complexes is not availablein Mat erialsSt udio (see Computa tional Deta ils), and w eha ve opted for a man ual a pproach to determine whetherCr spin sta te is conserved or a ltered during the cata lyticcycle. Five model sta t ionary points in the proposedmechanistic cycle (Figure 1) were identified as repre-senta tive structures for the spin stat e ana lysis, viz., theCr(II) ethy lene coordinat ion complex (M1), the Cr(IV)five-membered meta llacycle (M2), the direct Cr(IV)seven-membered metallacycle product (M3), the transi-tion structure for metallacycle formation (M1-2), a ndthe t ra nsi t ion st ructure for metal lacycle growth (M2-3), i llustrated in Figure 3.

The selected transi t ion state geometries representexamples of both a change of oxidation state of Cr [fromCr(II) t o C r(IV), M1-2] and conservation of oxidationsta te of Cr [(Cr(IV), M2-3] during t he respect i v et ransform at i ons . Bot h 5- a n d -bonding modes ofpyrrole wer e explicitly considered for a ll five geometr ies.For the Cr(II) complexes, M1a nd M1-2, three spinstates (singlet , triplet , and quintet) were considered,while two spin states (singlet and triplet) were consid-ered for the Cr(IV) species, M2, M2-3, a n d M3, ef-fectively representing all possible multiplicities. Fullequilibrium a nd t ra nsition st at e geometry optimizationswere performed both without fractional occupation (nos m ea r i n g) o f or b it a l s a t t h e F er m i l ev el a n d w i t hspecifying a t herma l smearing r a nge of 0.005 Ha to yielda total of 48 geometry optimizations.31 The relativecalculated electronic energies for the di fferent spinstates of these optimized geometries are summarizedin Table 1.

From the relative values in Table 1 it is evident thatthe triplet spin state represents the ground state for allequilibrium a nd t ra nsition stat e geometries considered.No structure for5-pyrrole quintet M1 could successfully

be optimized in which i t w as found t hat both ethylenemolecules spontaneously drift away from the Cr centerduring optimizat ion. This result is not sur prising sincethe num ber of ava ilable coordina tion sites in5-pyrroleM1 is exceeded by 1 (assuming a preferred octahedral6 s i t e a r r a n g e m e n t ) i n t h e h i g h q u i n t e t s p i n s t a t e ,effectively elimina ting the possibility for t he proposedstructure to exist . The smallest di fference in relat ives pi n s t a t e e ne rg ie s i s f ou n d f or t h e -pyrrole M1geometry in wh ich the singlet s tr uctur e is 2.9 kca l/mol

(28) (a) C acelli, I .; K eogh, D. W.; P oli, R.; Rizzo, A. New J. Chem.1997, 21, 133. (b) Cacelli, I.; Keogh, D. W.; Poli, R.; Rizzo, A. J. Phys.Chem. A 1997, 101, 9801.

(29) (a) P oli, R.; Ha rvey, J . N. Ch em. Soc. Rev. 2003, 32, 1. (b) Gr een,J . C.; H ar vey, J . N.; Poli , R.J . Chem. Soc., Dalton T rans.2002, 1861.(c) Ha rvey, J . N.; Aschi, M.; S chwa rz, H .; Koch, W. Theor. Chem. Acc.1998, 99, 95.

(30) Schroder, D.; S ha ik, S.; S chwa rz, H . Acc. Chem. Res. 2000, 3 3,139.

(31) Although not a lluded to here, s ubtle differences in geometricalparameters for complexes optimized at different spin states were found.Coordinates for all these geometries optimized at different spin sta tesare included in the Support ing I nformation.

Figure 3. Equilibrium and transit ion s ta te geometriesconsidered in multiplicity analysis.



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higher a nd t he quint et st ructure 3.5 kca l/mol higher inenergy compar ed to the triplet geometry . In a ll the oth ercases t he a l t ernat i v e spin s t a t es w ere s ignif icant l yhigher in energy (10.6-25.9 kcal/mol) compar ed to th epreferred triplet geometries. Relative energies obtainedfor the quintet transition structures, M1-2, were foundto be significantly higher in energy compared to boththe singlet and triplet optimized geometries, effectivelyshowing tha t th e highest spin sta te does not necessarilyrepresent the most fa vored spin sta te for Cr complexes.Geometry optimizations for the singlet -pyrrole com-

plex M3 and t he qui nt et -pyrrole transition structureM1-2, as indicated in Table 1, could not successfullybe optimized wh en integer va lues for orbita l occupationsof elect rons a t t he Ferm i l evel ( no sm eari ng) w ereenforced. I n b ot h cases t he SC F i t erat i ons di d notconv erge. How ev er, i t i s evi dent f rom t he rela t i v eenergies ca lculat ed for fra ctiona l electron occupa tion a tthe Ferm i level (0.005 Ha smea ring) tha t t he triplet spinst at e prev ai ls as ground s t a t e t hroughout . A generalcomparison of relative spin state energies calculated foral l speci es i n Tab l e 1 show s t hat essent i a l ly sm al ldifferences ar e found betw een relative energies obta inedw i t h (0. 005 H a ) a n d w i t h ou t s m ea r i n g. F r om t h ismultiplicity a na lysis we thus conclude tha t in our study

a t riplet spin sta te is conserved throughout t he proposedmechan ist ic cycle. Furth ermore, the use of a thermalsmearing ra nge of 0.005 Ha wa s found to yield energydifferences similar to t he energies where n o smearingwa s specified, effectively prompting the use of therm a lsmearing for all geometry optimizations discussed in therem ainder of t h i s paper. Thi s s t ra t egy ensured t heefficient convergence of SCF itera tions for a ll geometryoptimizat ions conducted.

Geometries. For th e calculated ethylene trimeriza-tion mecha nist ic cycle tw o bonding m odes of the pyr roleligand are explicitly considered for all optimized geom-etries, viz. , a 5- and -bonded pyrrole. In addition, astripped-down model , consist ing of only a Cl a tom a s

anionic fragment, and a full model, consisting of ClA-lM e3as a nion, a re investigat ed for both bonding modesof pyrrole. Geometries for the Cl models will be desig-nat ed asHxa nd Sxfor the respective5- a n d -bondingmodes of pyrrole, w hile the designat ions Hx a nd Sxwill be used for the ClAlMe 3models. In this section thegeometrical results obtained for the Cl models will bepresented first, followed by a brief comparison of dif-ferences in geometries obtained upon changing from theCl model to the full ClAlMe3 model.

The optimized geometries for 5-bonded pyrrole (Clmodel) participating in the proposed ethylene trimer-ization mecha nism a re illustra ted in Figure 4, while thecorresponding -bonded pyrrole geometries are illus-

tra ted in Figure 5. The Cr (II) speciesH1 is consideredas t he f i rs t ac t i v e i nt erm edi at e i n t he t r i m eri z at i oncycle. The optimized structure exhibi ts tetra hedralgeometry w ith Cr-P y and C r-Cl dist a nces of 1.927 a nd2.266 , respectively. The Cr center is in the planedefined by the four carbon atoms of the bonded ethylenemolecules, a nd each ethylene molecule is w eakly coor-dinated to Cr via -bonding interaction. The relativelyw eak nat ure of t he -bonding is reflected in the rela-tively short C-C bond distance of 1.381 , which is only0.045 longer than the calculated CdC dista nce in free

ethylene. Furthermore, the Cr-C dista nces for a singleethylene fra gment is n ot symmetr ica l, 2.245 and 2.331, respectively, with the carbon atom designated forcoupling w ith the other ethylene fra gment exhibi t ingthe longest Cr-C distance. The calculat ed Cr-N dis-ta nce in S1is 1.904 , and the Cl ligan d, as w ell a s thetwo ethylene fragments, is more t ightly coordinat ed toCr compared to H1. This relat ively contra cted na tureof t he l i gands i s a t t r i b ut ed t o a hi gher dem and forel ec t ron densi t y b y C r w hen pyrrol e i s b onded i n a-mode, in accord with the coordinatively unsaturatednat ure of Cr for -pyrrole (vide infra). Another signifi-cant difference in the geometries of H1 a nd S1 i s t hemore pronounced piano-stool geometry for t he former,

in which the Cl and ethylene fragments are bent awayfrom the pyrrole ligand.Forma tion of th e five-membered meta llacycle Cr (IV)

species H2 is afforded by oxidative a ddit ion of the twoethylene fragments via the tra nsi t ion str ucture H1-2.I n H1-2 the coupling C-C distance is decreased from2.598 in H1 to 1.898 , while contraction of the 5-bonded pyrrole ring in the transi t ion state is evidentfrom the changes in Cr-Py distance from 1.927 f1.912 f1.968 in the sequence H1fH1-2fH2.The transition structure for metallacycle formation oft he -bonded pyrrole model, S1-2, points to a signifi-cantly earl ier transi t ion state, as is evident from therelatively longer C-C coupling distance (2.034 ) and

larger C-C r-C a ngle (123.4) compar ed t oH1-2. Thefive-membered metallacycle products, H2 a nd S2, haveC-C coupling dist a nces of 1.529 a nd 1.536 , r espec-tively, which is in agreement with the expected distancefor C-C single bonds. For both H2 a nd S2 t h e C r-C la n d C r-Py distances are shorter for the Cr(IV) com-plexes compa red to t he dista nces obta ined for t he Cr(II)complexes H1 a nd S1.

In order for ethylene trimerizat ion to proceed, theincorporat ion of a third ethylene molecule is necessa ry.Interaction of ethylene with the five-membered metal-lacycle H2 affordsH3, in w hich t he ethylene fragmentis weakly coordinated via a long-range -interaction.Thi s i s evi dent f rom t he elongat ed C r-C di st anc es

Table 1. Relative Electronic Energies for Different Spin States of M1, M1-2, M2, M2-3, and M3 in kcal/mol(values in parentheses are calculated with a thermal smearing range of 0.005 Ha)

M1 M1-2 M2 M2-3 M3

5-pyrrole singlet 16.4 (15.1) 9.9 (9.3) 15.2 (14.1) 17.1 (14.9) 12.2 (11.5)t r iplet 0.0 (0.0) 0.0 (0.0) 0.0 (0.0) 0.0 (0.0) 0.0 (0.0)quintet a 25.9 (25.9)

-pyrrole singlet 2.9 (2.9) 15.7 (11.5) 19.4 (17.8) 10.6 (10.5) b(15.7)t r iplet 0.0 (0.0) 0.0 (0.0) 0.0 (0.0) 0.0 (0.0) 0.0 (0.0)q uint et 3.5 (3.4) b(22.0)

a No structure could successfully be optimized for quintet M1 due to the lack of sufficient coordination sites on Cr(II) in the highestquintet spin state. In all efforts both ethylene molecules spontaneously drifted away from the Cr center. b SCF did not converge when nosmearing wa s specified.



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(2.464 and 2.586 ) for Cr-ethylene in H3, a s w e ll a sthe relat ively short CdC distance of 1.355 for thecoordinated ethylene fragment. The significantly en-dothermic nature (vide infra) of ethylene coordinationt oH2, t o yield t he 16-electr on speciesH3, corrobora testhe fact that Cr complexes tend to favor a low electron

count in the valence shell . This is also evident fromunsuccessful efforts to optimize a geometry similar toH3 for -b onded pyrrol e; each a t t em pt l ed t o t hespont a neous di ssoci at i on of e t hylene from t he 10-electron species,S2, during optimization. It is t hereforeproposed that H3 represents a shallow local minimumon the PES for effective concerted metallacycle growthfrom H2 t o H4. I nsert ion of the coordinat ed ethylenef r a g me nt i nt o t h e C r-C 3 b o n d , a n d n o t t h e C r-C 6bond, of H3 is suggested from t he elongat ed na ture ofC r-C3 (2.177 ) compa red to C r-C6 (2.137 ). Metal-lacycle growth (H3fH3-4fH4) to yield t he seven-membered metallacycle, H4, proceeds by insertion ofethylene into the C r-C3 bond via the tra nsi t ion struc-

t ureH3-4. I n H3-4 formation of the Cr-C1 (2.196 )a n d C 2-C3 (2.243 ) bonds a nd ruptur e of the Cr-C 3(2.362 ) bond a nd C1-C2 (1.406 )-bond proceed ina concerted fashion. In H4 t he C r-C1 bond relaxes t o2.058 . A transi t ion structure similar to H3-4w a ssuccessfully optimized for a -bonded pyrrole complex

(S3-4). In S3-4 the C2-C3 d ista nce (2.279 ) is foundt o b e s i m i l ar c om pared t o H3-4, w h i l e t h e C r-C 3di st anc e (2.181 ) i s s ignif icant l y short er and ac -compan ied by an a gostic intera ction (2.012 ) betweenCr a nd a hydr ogen on C3, which is not observed forH3-4. This addit ional bonding interaction found for the-bonded model reflects a compar a tive la ck of electrondensity at the meta l center in the tra nsition sta te, whichis not necessarily attributable to the relatively smallerformal n umber of va lence electrons in S3-4 comparedt o H3-4 (see discussion for str ucture H7).

In order for t he liberat ion of 1-hexene to proceed fromthe seven-membered met alla cycles,H4 a nd S4, reduc-tive-hydr ogen migra tion from C2 to C6 (or from C 5 to

Figure 4. DMol3/G G A/P W91/DN P optimized sta tiona ry points for 5-pyrrole Cl models.



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C 1) needs t o t ake plac e. I nspect i on of t he carb onbackbone geometries in H4a nd S4 reveals, however,t hat none of t he -hydrogens are ideally positioned toafford facile -hydrogen migration. Sequential confor-mational changes from H4 a nd S4, involving first anal terat ion at C5 (via transi t ion structures H4-5a ndS4-5 to y ield H5 a nd S5, respectively) and second anal terat ion at C3 (via transi t ion structures H5-6a nd

S5-6 to yield H6 a nd S6, r espectively), a fford seven-membered metal lacycle geometries resembling boatconformations in which both C2 and C5 contain axial-hydr ogens suita ble for-hydrogen migration. In thismechanistic study migration of the axial -hyd rogen onC2 to C6 of H6 a nd S-6 was considered for all models.

Migration of the a xial -hydrogen of C2 in H6 t o C 6l ea d s t o t h e f or m a t i on of a n a g os t ic i nt e r me di a t estructure H7 v i a t he t ransi t i on s t ruc t ure H6-7. I nH6-7 t h e C 2-H distance elongates to 1.151 , whilethe corresponding C r-H, C 1-C2, and H-C6 dista ncesdecrea se t o 1.916, 1.499, a nd 2.347 , respectively. TheC 2-H , C r-H , C 1-C 2 , a n d H-C 6 di s t anc es rel ax t o1.186, 1.750, 1.472, and 2.011 , respectively, in the

-agostic intermediateH7. All att empts to optimize a nagostic intermediate similar to H7 for t he -bondedpyrrole model wa s unsuccessful; each at tempt r esultedin the spontaneous formation of S6. This result is incontr ast to the agostic intera ction tha t w a s observed for-pyrr ole in S3-4, b ut n ot f or H3-4. Cr-mediatedhydrogen m i grat i on from C 2 i n H7 t o C 6, v ia t h etra nsi t ion structureH7-8, yields 1-hexene coordin a ted

to the resulting Cr(II) center (H8) via -bonding inter-a c t ion a t t h e d o ub le b on d a n d a r em a i n in g a g os t icinteraction w ith th e migrated hy drogen. Similar a gostic-assisted hydrogen migration transi t ion structures forethylene trimerizat ion with Ta and Ti catalysts wererecently calculated and reported.11,12 InH7-8 the Cr-H(1.637 ), C 2-H (1.360), and C6-H (1.549 ) distancessuggest t hat t he t ra nsit i on s t a t e i s ra t her earl y a nd i sm ore reac t ant (H7) like. This is in contrast to the Cr-mediat ed hydrogen migration tra nsi t ion st ructure op-timized for th e-bonded pyrrole model (S7-8) in w hicht he C r-H (1.627 ), C2-H (1.482 ), and C6-H (1.463) distances suggest a la ter tra nsi t ion sta te tha n H7-8, which resembles the product (S8) more closely th a n

Figure 5. DMol3/G G A/P W91/DN P optimized sta tiona ry points for -pyrrole Cl models.



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t h e r e a g en t (S6). A s i gnif icant decrease i n C r-P ydistance upon following the sequence H6 f H6-7 fH7fH7-8fH8 of 1.981 f1.960 f 1.914 f1.909 f1.902 is found, effectively suggesting tha tcontraction of the 5-bonded pyrrole ring favors -hy-drogen migra tion. A similar decrease in C r-N distancefor S6fS7-8fS8 is not found, which may relat e tothe significant differences found in activation energiesfor -hydrogen migration for - and 5-bonded pyrrole(vide infra).

Expansi on of t he C l m odel s t o c ont ai n an ani oni c

fragment consist ing of trimethylaluminum chloride(ClAlMe3) w a s considered for a l l geom et ries i n t heethylene trimerization mechanistic sequence. A selec-tion of optimized geometries for these expanded modelsis i l lustrated in Figures 6 and 7 for 5- and -bondedpyrrole, respectively. Comparison of the optimized Clmodel structure H1 wi th the corresponding ClAlMe3model structure H1 show s el ongat i on of t he C r-C ldistance by 0.064 and a Cl-Al coordinat ion dista nceof 2.530 . The elongation of the Cr-Cl distance uponexpansion of Cl to ClAlMe3 is a genera l trend observedfor a ll optimized geometries for both bonding modes ofpyrrole. A slight decrease in coordination distances ofthe pyrrole l igand and tw o ethylene fragments is found

between H1 a nd H1, w h i ch on ce a g a i n f ol low s aconsistent trend for Cr-l igand distances for al l geom-etries considered in the mechanist ic cycle. For mosttransition structures no significant geometrical differ-ences are observed between the Cl and ClAlMe3models.However, a significa ntly less pronounced a gostic inter-action betw een Cr-H (2.388 ) is observed for S3-4compared toS3-4 (2.012 ), which allows for a longerC r-C3 (2.259 ) and short er Cr-C1 (2.113 ) dista nce

in S3-4

compared to Cr-C3 (2.181 ) and Cr-C 1

(2.228 ) in S3-4. The more favorable nature of theS3-4 geometry compared to S3-4 is reflected in therelat ively lower activa tion energy observed in this stepfor the ClAlMe3 model compared to the Cl model for-pyrrole (vide infra). Similarly, the relatively shorterC 2-H distance (1.108 ) and longer Cr-H di s t anc e(2.647 ) in the transition structure H6-7compa redto the corresponding d ista nces inH6-7(1.151 and 1.916, respectively) suggest th at the former tra nsition stat e(ClAlMe3model) is significantly earlier compared to thecorresponding t ra nsi t ion sta te for the Cl model . Nev-erth eless, most g eometr ical differences found for5- a n d-bonded pyrrole in the Cl models are effectively repro-

duced for t he different bonding modes of pyrrole in themore rea listic ClAlMe3 models.

Electronic versusGibbs FreeEnergies. The C r(II)structures H1, S1, H1, a n d S1 have been chosen asreference structures to which the energies of all station-ar y points in the mechanist ic sequence ar e related a ndcorrected with the relevant number of ethylene mol-ecules. The DM ol3/G G A/P W91 poten tia l energ y su rfa ces(PESs) for the two Cl models and two ClAlMe 3models,i .e. , for 5- a n d -bonded pyrrole in each case, a rei ll ust rat ed a s four separa t e energy l ev el di agra m s i nFigure 8. In each case the relat ive electronic energydifferences (without the inclusion of zero-point energycorrections a nd designat ed a s E) and rela t i v e v ari a-tions in calculated G ibbs free energy corrections t o theelectronic energies (with the inclusion of ZPE correc-tions), for all stationary points in the proposed mecha-nism, are i llustrat ed. Two temperatures for the G ibbsfree energy corrections, viz. , 298.15 a nd 375.00 K, a reconsidered for each graph and are designated by G298a nd G375, respectively.

A comparison of the electronic (E) and Gi b bs f reeenergy (G298 a nd G375) differences for 5-bondedp y r r o l e i n t h e C l m o d e l ( graph a i n Fi gure 8) show sessentially no differences for the metallacycle formationsequenceH1fH1-2fH2, for w hich similar a ct iva-tion (Ea ) 9.7, Gq298 ) 10.4, and Gq375 ) 10.7 kca l/

mol, respectively) a nd rea ction energies (E) 2.0, G298) 1.9, and G375 ) 2.2 kcal/mol, respect ively) ar e found .In contr a st, however, the metalla cycle growt h sequenceH2fH3-4fH4 shows significan t differences for bothcalculated act ivat ion (Ea ) 13.4, Gq298 ) 29.1, andGq375 ) 32.9 kcal/mol, respectively) an d rea ction ener-gies (E) -20.9, G298 )-5.6, and G375 )-2.4 kca l/mol, respectively) between the relative electronic andGibbs free energy values. The relatively less favorablereaction a nd a ctivat ion G ibbs free energies a re at tribut-able to unfavorable entropy (TS) corrections to thetotal electronic energies when an addit ional ethylenemolecule is introduced to the mechanism and insertedinto th e five-membered meta llacycle structur eH2 (vide

Figure 6. DMol3/G G A/P W91/D NP optim ized st a ti ona rypoints for 5-pyrr ole C lAlMe3 models.



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infra). An essentially constant difference between cal-culated total electronic energies (E) and Gi b b s f reeenergies (G298 a nd G375) of ca. 15 a nd 18 kcal/mol,

for G298 a nd G375, respectively, is found t o be ma in-t ai ned for t he rest of t he m echani st ic sequence H4through H8.

Figure 7. DMol3/G G A/P W91/DN P optimized sta tiona ry points for -pyrr ole C lAlMe3 models.

Figure 8. Comparat ive E, G298, a n d G375 DMol3/G G A/P W91/DN P poten tia l ener gy su rfa ces for 5- and -pyrrole forboth the stripped-down Cl and full ClAlMe 3 anion models.



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Ca lculat ed rea ction a nd activat ion electronic energies(E), a s w e ll a s t h e cor r es pon d in g e nt h a l py (H),entropy (TS), and Gibbs free energy (G) correctionsa t 298.15 K, for meta llacycle forma tion an d meta llacyclegrowth (for both the C l a nd ClAlMe3 models a nd bothbonding modes of pyrrole) are summa rized in Ta ble 2.From Table 2 it is evident that the TS298contributionsto t he calculat ed G ibbs free energies for meta l lacycleformation is negligible (-1.1 t o 0.5 kcal/mol), wh ichrelat es to the similar meta llacycle forma tion H298a ndG298values a ccording to the rela tionG) H - TS.

In contra st , however, relat ively large negative T

S298contributions (-14.1 to -12.4 k ca l/mol) t o G298 form et a l la c ycl e g r ow t h a r e f ou n d . A s im il a r t r en d i sobserved for the relat ive calculated act ivat ion energypara meters in which the TSq298cont ributions to Gq298are negligible for metallacycle formation (-2.0 to -0.4kcal/mol), but significa ntly nega tive for meta llacyclegrow t h (-14.5 to -13.6 kcal/mol). These unfa vora bleentropy contributions arise from the incorporation of anadd itiona l ethylene molecule during metalla cycle growth,essential ly converting a bimolecular system to a uni-molecula r system. The effective Gibbs free energies ofac t i vat i on (Gq298) for m et al lac ycl e grow t h, i n , forexample, the ClAlMe3 sequence H2 f H3-4, show

tha t considera tion of only electr onic energy differenceswould lead to a 15.8 kca l/mol underestima tion of th eactivation energy determined for Gq298 and serv es t oemphasize the importance of inclusion of free energycorrect i ons t o t he cal cul at ed energy di fferences. Asim i lar i ncrease i n t he est i m at i on of t he effect i v emeta llacycle growth a ctiva tion energy by 11.3 kcal/mol,upon inclusion of thermodynamic corrections at 298.15K, is reflected in t he recently reported DFT study onTi-cata lyzed ethylene trimerization by de B ruin et a l.11b

A general comparison of the gra phs in F igure 8 showstha t an increase of temperature from 298.15 to 375 Kha s no significa nt effect on calculat ed G ibbs free energydifferences for metal lacycle forma tion. Metal lacycle

growth is, however, calculated to proceed with a slightlyhigher act ivat ion energy for a l l four mechan isms rep-resented in Figure 8. This increase in Gq375 comparedt o Gq298 r e su lt s f r om a n i ncr ea s e i n t h e n eg a t i veentropy contribution (TSq375) t o Gq375 relat ive to theTSq298 contribution to Gq298 (not included in Table2).

The rela tively consta nt Gcorrection ra tios obta inedfor the di fferent models are evident from the similargra phs in Figure 8. Consequently, th e Gibbs free energydifferences a t 298.15 K (G298) w i l l b e used for a l lenergy and mechanistic comparisons among stationarypoi nt s i n t he rem ai nder of t h i s paper. The rel a t i v eenergies for 5- and -bonded pyrrole will be compared

for t he Cl model, followed by a brief discussion on thedifferences obtained w ith expansion t o the C l A l M e 3model. C om parat i v e P ES s (G298) for 5- an d -bondedpyrrole are i l lustrated in Figures 9 and 10 for the Cland ClAlMe3 models, respectively. Note that in eachcase the energies of all sta tionar y points a re referencedto th e respective calculated G298values for H1 (Figure4) an d H1(Figure 6).

5- versus-Bonded Pyrrole: Metallacycle For-mation. Metallacycle formation for 5-bonded pyrrolefrom H1 t o H2 (Figure 4) is ca lculat ed to be endothermic

Table 2. Reaction (E, H298, TS298, andG298) and Activation (Ea, Hq298, TSq298, andGq298)Parameters (kcal/mol) for Metallacycle Formation and Metallacycle Growth for Both the Cl and

ClAlMe3 Models

reaction step E Ea H Hq TS TSq G Gq

H1fH1-2fH2 2.0 9.7 0.8 9.3 -1.1 -1.1 1.9 10.4S1fS1-2fS2 -9.3 9.6 -9.1 9.7 -0.7 -1.6 -8.4 11.3H1 fH1-2 fH2 5.5 9.1 4.6 9.1 0.5 -0.4 4.0 9.5S1 fS1-2 fS2 -8.0 9.5 -7.4 9.4 -1.2 -2.0 -6.2 11.4H2fH3-4fH4 -21.0 13.4 -17.9 14.6 -12.4 -14.5 -5.6 29.1S2fS3-4fS4 -24.7 18.7 -22.2 19.2 -13.2 -14.0 -9.1 33.2

H2fH3

-4

fH4

-23.1 9.2 -20.4 11.1 -14.1 -13.9 -6.3 25.0S2 fS3-4 fS4 -25.7 7.3 -22.6 8.3 -12.8 -13.6 -9.8 21.8

Figure 9. Relat ive G298 DMol3/G G A/P W91/D NP pot en -tial energy surfaces for 5- and -pyrrole for t he C l a nionmodels (kcal/mol). All ener gies a re rela tiv e to H1 correctedwith the relevant number of ethylene molecules . Energydifferences between two stationary points are indicated initalics.

Figure 10. Relative G298DMol3/G G A/P W91/D NP pot en -tial energy surfaces for 5- and -pyrrole for the ClAlMe3an ion models (kcal/mol). All energies ar e r elative to H1corrected wit h t he relevant number of ethylene molecules.

E n er gy di ff er en ces b et w een t w o s t a t ion a r y p oin t s a r eindicated in italics.



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by 1.9 kcal/mol and requires a modest a ctivat ion ba rrier,

via transi t ion structure H1-2 (Figure 4), of 10.4 kcal/mol (Figure 9). The preferred conformation of the five-membered ring of H2 is dicta ted by the r elat ive orien-t at i on of t he et hyl ene fragm ent s i n H1 a nd H1-2.Alterna tive conforma tions for H1, H1-2, and H2 w erealso optimized and are i l lustrated as H1-alt, H1-2-alt, a n d H2-alt in Figure 11. The calculated changesin G298for H1fH2 a ndH1fH1-2-alt are 1.8 and10.9 kcal/mol, respectively, wh ich is essent ia lly simila rto the energies calculat ed forH1fH2 a nd H1fH1-2. I t w as c onsequent l y dec i ded t o onl y c onsi der t heconformation as represented for H2 as active intermedi-a te in t he mecha nistic cycle. The meta llacycle precursorfor -bonded pyrr ole, S1 (Figu re 5), is 1.2 kca l/mol

higher (Figure 9) in energy compared to H1, whichsuggest s t ha t t he 5-bonded mode of pyrr ole w ill ther-m odynam i cal l y b e fav ored a t t he s t a r t of t he m echa-nism. The compara tive a ct ivat ion energy for metal la-cycle forma tion for -bonded pyrrole is slight ly h igher(11.3 kcal/mol) compa red to 5-bonded pyrrole (10.4 kcal/m ol ) , w hi c h i s i n c ont rast t o t he s i gni f i c ant l y m orefavorable reaction energy for S1fS2 (-8.4 kca l/mol)compared to H1fH2 (1.9 kcal/mol). Conseq uen tly ,S2is 9.1 kcal/mol lower in energy th a nH2, which suggestst h a t t h e -bonded mode of pyrrole will t hermodyna mi-cal ly be favored for the five-membered metal lacycle.Forma tion of t he five-membered meta llacycle involvesan oxidative addit ion process in which the oxidation

state of Cr formally changes from II to IV.5-versus-BondedPyrrole: MetallacycleGrowth.

At this stage of the mechanism a competition betweenmetallacyclopentane (H2 a ndS2) decomposition, to yield1-butene, and metallacycle growth upon incorporationof an addit ional ethylene molecule may be envisaged.However, 1-butene forma tion from metal lacyclopen-ta nes wa s found to be disfavored compared t o metal la-cycle growth in theoretical studies for Ti-11 and Ta-catalyzed12 ethylene t rimerizat ion. In these studies i twas found that 1-butene l iberat ion from the metal la-cyclopentanes proceeds in a two-step mechanism whichrequires higher a ct ivat ion and reaction energies com-pared to meta llacycle growth. These relatively unfa vor-

ab l e energi es are a t t r i b ut ed t o t he r i ng s t ra i n of t hemeta llacyclopenta nes. Therefore, reaction st eps for com-peting 1-butene liberation from either H2 a nd S2werenot considered in this study.

In order for meta llacycle growth to occur fromH2 a na dditional ethy lene molecule needs to intera ct with C r.Et hylene coordina tion to Cr inH2 leads to the format ionof t he w eak -complex H3 and is found to be signifi-cant ly endothermic by 21.4 kca l/mol (Figure 9). Thisrelat ively high endothermici ty is at tributable to twofactors, viz. , a n unfa vorable entropy contribution to theGibbs free energy for this step in the mechanism andthe unprecedented nature of seven-coordinated Cr com-plexes mentioned t o ear lier (vide supra ). Consequent ly,

H3 is regarded a s a sha llow loca l minimum on the pat hof effective concerted ethylene insertion in the Cr-C 1bond of H2. All efforts to optimize a -pyrrole complexsimilar t o H3 resulted in the spontaneous dissociationof the ethylene fra gment from the complex, essentia llysuggesting that incorporation of ethylene in S2 will beless favora ble compared t o incorpora tion of ethylene inH2. Once aga in, the coordinat ion mode of t he pyrrolel igand seems t o dicta te t his discrepancy.

The relat ively longer Cr-C2 distance (2.586 ),compared to Cr-C1 (2.464 ) in H3, a s w e l l a s t h erelat ively longer Cr-C3 (2.177 ) versus Cr-C6 (2.137) dista nce, suggest coordinat ion of C2 wit h C3 dur ingmetallacycle growth. A transition structure (H3-4) for

C 2-C3 coordina tion in H3 connects H3 a nd H4 w i t h aba rr ier of 7.7 kca l/mol an d a n exother micity of 27.0 kca l/mol. Alternative coordination of C1 and C3 in H3 w a sa l s o c on s id er ed a n d l ea d s t o t h e f or m a t i on of t h etransi t ion structure H3-4-alt and seven-memberedmeta llacycle product H4-alt i l lustrated in Figure 12.The increa se in energy for H3 fH3-4-alt, however,is 6.9 kca l/mol high er compa red t o H3fH3-4, makingthis mode of ethylene insert ion less probable. Theeffective gain in energy for metallacycle growth H2 +ethylene fH4 is 5.6 kcal/mol wit h a n effective a ctiva -t ion ba rrier (H2+ ethylene fH3-4) of 29.1 kca l/mol,essentially representing the rate-determining step in the5-pyrrole mechan ism (Figure 9). This estima ted ba rrier

Figure 11. DMol3/G G A/P W91/DN P optim ized st ru ctu resof H1-alt, H1-2-alt, a n d H2-alt. Figure 12. DMol3/G G A/P W91/DN P optim ized st ruct ur es

of H3-4-alta n d H4-alt.



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is slightly higher than the barrier reported (23.3 kcal/m ol ) for t he s im i lar effect i v e t ra nsform at i on i n t hecalculated Ti-catalyzed trimerization of ethylene.11b

The sequence S1f S3-4 f S4 proceeds with ana ctiva tion ba rr ier of 33.1 kcal/mol, for concerted inser-tion of ethylene into the Cr-C1 bond of S2 (Figure 5),an d is exothermic by 9.1 kcal/mol. This meta llacyclegrowth a ctivation barrier represents t he rat e-determin-ing step for th e-pyrrole mecha nism. A direct compar i-

son of the relative energies for H3-4 a ndS3-4 (Figure9) shows that S3-4 is lower in energy than H3-4 by5.1 kca l/mol. This effectively su ggest s th a t t he -coor-dinated pyrrole geometry wil l preferential ly populat et h e t r a n s it i on s t a t e f or m et a l la c ycl e g r ow t h i n t h eproposed mechanism. I t is interesting to note that anagostic interaction between Cr and a hydrogen on C3is present in S3-4, accompanied by a relatively shortC r-C3 dista nce, not found for H3-4. A-bonded modeof pyrrole is also preferred for the seven-memberedmetallacycle product,S4, wh ich is found t o be 12.6 kca l/mol lower in energy compared to H4.

5- versus -Bonded Pyrrole: 1-Hexene Libera-

tion. 1-Hexene libera tion from t he direct m eta llacyclegrowth products,H4 a nd S4 (Figu res 4 a nd 5), could inprinciple proceed by reductive -hydrogen migrationfrom C2 t o C6 (or s imilarly fr om C5 t o C1). None of the-hydrogens inH4 a ndS4do, however, ha ve a preferredaxial orientation necessary to ensure facile -hydrogenmigration. Consequently, the potential energy surfacesof these seven-membered metallacycle intermediatesw ere i nv est i gat ed i n m ore det ai l b y c onsi deri ng ad-dit ional conforma tions of the seven-membered ring.Downwa rd rota t ion of C5 in H4 (and S4) via transitionstructure H4-5 (and S4-5) leads to the format ion ofthe m etallacycle intermediate H5 (andS5), in w hich oneof the-hydr ogens on C5 is positioned in a formal a xial

orientation. The activation energies for the conforma-tional changes H4fH5 a nd S4fS5 ar e 6.8 and 5.8kcal/mol, respectively, wit h rea ction energies -0.7 and1.3 kcal/mol, respectively. A second subseq uent confor-m at i onal change considered i nvol ves t he dow nw a rdrotation of C3 in H5 (and S5), via t ra nsi t ion str uctureH5-6 (and S5-6), to yield th e semi-cha ir geometr y H6(and S6). The activation energies for this second con-forma tional change a re 9.6 a nd 5.6 kcal/mol for therespective 5- a n d -bonded modes of pyrrole, withrespective reaction energies of -0.4 an d -1.8 k ca l/mol.After this second conformational change a -hydrogenon C-2 in H6 (and S6) is forma lly axia l, representing a

conforma tion suita ble for -hydr ogen migra tion from C2.The semi-chair conformations for the seven-memberedrings in H6a nd S6 are dist inguished from the otherconformations (H4, H5, S4, a n d S5) by t he sequentialt r a n s orientations of axial hydrogens upon following thesequenc e C 1 t o C 6 and are anal ogous t o t he l ow estenergy chair conforma tion for cyclohexane. S imilarsemi-chair conformations for seven-membered metalla-cycl e s t ruct ures w ere a l so expli ci t ly consi dered i ncalculated ethylene trimerizat ion mecha nisms cata lyzedby Ti11 and Ta.12 The relatively lower energies obtainedfor all-bonded pyr role seven-membered m eta llacycles,as w ell as rela t i vely l ow er ac t i vat i on energies forconform at i onal changes, com pared t o t he 5-modes,

s u g g e s t t h a t t h e -bonding mode of pyrrole wil l bepreferred in this region of the potentia l energy surfa ce.

Although -hydrogen migration may proceed fromeither C2 or C5 to C6 and C1 (in H6 a nd S6), respec-tively, only t he migra tion from C2 to C6 w as consideredin this mechanistic study. Significant energy differencesar e not envisaged for a l ternative-hydr ogen m igra tionfrom C5 to C1. -Hydrogen migration in H6 leads t othe format ion of an a gostic sta bilized intermedia te, H7,

via the transi t ion structure H6-7, wi th a low barrierof 4.6 kcal/mol a nd a rea ction ener gy of 0.7 kcal/mol.Subsequent continua tion of Cr-mediated -hydrogenmigrat ion from H7proceeds via the tr an sition str uctureH7-8, w hich is calcula ted to be 0.5 kca l/mol lower inenergy than H7.32 -hydr ogen migra tion involves r educ-tive elimination of the Cr(IV) H6 species to the corre-sponding Cr(II) species, H8, i n w hi c h t he l i b erat ed1-hexene fragment is coordinat ed to Cr via a -interac-tion a t t he double bond a nd a n a gostic intera ction withthe migrated hydrogen of C6. To ascertain whether theformation of the agostic intermediate geometry, H7, isa prerequis it e for t he t ransform at i on H6 f H8, a nintrinsic reaction path (IRP) calculation involving H6

(reactant), H7-8 (tra nsi t ion structure), a nd H8 (prod-uct) was performed. From the PE S ma pped by the IRPcalculation it was found tha t H7-8 is directly connectedto th e product H8. In contra st , however, an addit ionalequilibrium geometry between H6 a nd H7-8 w a sidentified that corresponded toH7. This result empha-sized that a stepwise pat hwa y H6fH7fH8 operatesfor 5-pyrrole in this r egion of the PE S, in contrast tot he resul t s ob t ai ned for -pyrrole (vide infra ). Theenergy gain for the transformation H7 f H8 is 16.8kcal/mol, while the g a in in energy for the sequenceH6fH8 is 16. 1 kca l/mol.

Similar Cr -mediated -hydrogen migration in S6 w a scalculated to proceed in a concerted fashion via the

tra nsi t ion structure S7-8 to t he 1-hexene complexS8.N o a gost i c s t a b il iz ed i nt erm edi at e for t he -bondedpyrrole model , similar to H7, was successful ly opti-mized, which is in contrast to the agostic interactionfound for S3-4, but not for H3-4. IRP calcula tions forS6 (reactant), S7-8 (tra nsi t ion structure), and S8(product) confirmed tha t S7-8 is directly connected toboth S6 a nd S8. Another interesting observation fromt hi s I RP cal cul at i on w a s t hat rot a t i on of t he pyrrol ylfragment in S7-8 relat ive to the pyrrolyl orienta t ionin S6a nd S8 takes place spontaneously (Figure 9).Several efforts to optimize a t ra nsi t ion st at e geometrythat resembles the pyrrolyl orientat ion in S6a nd S8were unsuccessful; in each instan ce the tra nsition stat e

search converged to the S7-8 geometry. The energybarrier for the transformationS6fS8is 14.5 kca l/mol,which is significantly higher than the effective barrierfor H6 f H8 (4.6 kca l/mol). In a ddit ion S6f S8i sendoth ermic by 0.9 kcal/mol, which is in sha rp cont ra stto t he exothermic tra nsforma tion ofH6 fH8 by 16.1kcal/mol. The r elat ively lower energ y of H8 comparedt oS8 (by 5.0 kcal/mol) represen ts one of the few a rea s

(32) The lower G298energy of H 7-8 compared toH7 is explainedby the relative thermodynamic corrections to the electronic energiesof the respective species. Considera tion of purely electronic energiess h o w s t h a t t h e e n e r g y o f H7-8 is 1.5 kcal/mol higher in energycompared to H7. The tota l correction t o the electronic energy a t 298.15K for H 7-8 is 15.1 kca l/mol, wh erea s th e corres ponding correction forH7 is 17. 1 kca l/mol.



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on t he pot ent ia l energy surfac e w here a 5-bondedpyrrol e i nt erm edi at e i s m ore s t ab l e t han t he c orre-sponding -m ode. I n general t h i s suggest s t hat t heCr(II) intermediat es prefer a 5-bonding mode of pyrr ole,wherea s the Cr(IV) intermediates prefer the alterna tive-bonding mode of pyrrole.

A s i gnif icant feat ure of t he t ransi t i on s t ruct uresH7-8 a nd S7-8 i s t he part i a l coordi nat i on of t hemigrat ing hydr ogen t o the Cr center, effectively empha-

sizing a migra tion process which is Cr-mediat ed. Similaragostic assisted hydrogen migrat ion m echan isms werereported by Yu et al. , 12 Blok et al.,11a and de Brui n eta l.11b for 1-hexene liberation in Ta- and Ti-catalyzedethylene trimerization.

The selectivity toward 1-hexene in the ethylene tri-m eriz at i on m echani sm i s regul at ed b y t he rela t i v eactivation energies for competing -hydrogen migrationin H6 a nd S6 compared to coordination and insertionof an additional (fourth) ethylene molecule in H6 a ndS6. From theoretical studies on Ti 11 and Ta 12 i t w a sfound that ethylene coordination and insert ion in re-spective meta l lacycloheptane intermediat es a re unfa-vorable compa red t o meta llacyclohepta ne decomposition

to yield 1-hexene. Eth ylene coordinat ion a nd insertionin metallacyclopentane inetermediates (H2 a nd S2) isfound t o b e part i c ul arl y unfav orab l e i n t he currentstudy. In addit ion, the relat ive act ivat ion energies for-hydrogen migration in H6 a nd S6 are fav orab l e .Consequently, a mechanism involving further metalla-cycle growth, to yield metallacyclononane intermediatesand 1-octene liberation, is not envisaged to be energeti-cal ly favorable and was not considered in the currentstudy.

General inspection of the potential energy surfacedepicted in F igure 9 shows th e overa ll ethylene trimer-izat ion t ra nsforma tions, H1 + ethylene fH8 a nd S1+

ethylenef

S8, a re exothermic by -

20.9 and -

17.0kcal/mol, respectively. This is in a greemen t w ith t he fa ctthat Cr-catalyzed trimerization is a facile process. Thera te-determining st ep in th e mecha nism is predicted tobe metal lacycle growth with Gqoverall ) 38.2 a nd 33.1kca l/mol for 5- a n d -bonded pyrrole, respectively.These Gqoverall values are both relat ed to the-pyrrolemetallacyclopentane geometry, S2, in Figure 9. This isbecause the5-pyrrole meta llacyclopenta ne, H2, wh ichis higher in energy tha n S2by 9.1 kca l/mol, is in ra pidequilibrium w ith t he reference stat e S2.

ClAlMe3 Models. Expansi on of t he C l ani on frag-ment t o a more rea listic ClAlMe3anionic fra gment wa sdeemed necessary to ensure closer resemblance of the

theoretical models to actual reagents used in experi-mental studies. The comparative potential energy sur-faces for the proposed ethylene trimerizat ion mecha-nism for the 5-bonding mode of pyrrole is illustratedi n F i g u re 13 f or b ot h t h e C l a n d C lAl Me3 models.Excellent agreement of calculated activation and reac-tion energies is evident for the two models. The com-parat i v e pot ent i a l energy surfac es for t he -bondingmode of pyrrole (for both the Cl and ClAlMe 3 models)are i llustrat ed in Figure 14. In contra st w ith th e goodag reement observed for5-bonded py rr ole models (Fig-ure 13), a conspicuous lower activation energy for S2fS3-4fS4(21.8 kca l/mol) compa red t o S2fS3-4f S4 (33.1 kcal/mol) is evident from Figur e 14. This

difference is a t tributed to significan t geometrical di f-ferences found for the optimized structures of S3-4a nd S3-4, a l l uded t o earl i er , i n w hi ch t he C l Al Me3fragment in S3-4enforces significa nt relative elonga-tion of the C r-Cl bond, which in turn results in morefav orab l e ac com m odat i on of t he i nsert ing et hylenefragment. This significant lowering of the act ivat ionenergy for metallacycle growth, upon expansion of thea n i on f r a g me nt f r om C l t o C l Al Me3, r ep r es en t s af un d a m en t a l l ow e r in g of t h e b a r r ie r of t h e r a t e -determining step in the overall proposed mechanism.This could in part point to the positive effect trialkyl-aluminums ha ve on t he Cr-cata lyzed ethylene trimer-ization.

Ring Slippage. In Figure 9 the relative energies ofa l l equil ib rium and t ransi t i on s t a t e geom et ries a represented, for both 5- and -bonding modes of pyrr ole,relat ive to the energy of the 5-bonded structure H1.From this representat ion a direct energy comparison

between similar structur es with different bonding modesfor pyrrole ma y be ma de. As pointed out ear l ier, met-allacycle formation is preferred for the H1fH1-2fH2 sequence due to the lower relat ive energy of H1versusS1, as well as the slightly lower activation energynecessa ry for meta llacycle format ion t o proceed from theformer. The significant ly lower energy ofS2 comparedt o H2 suggests, however, that a transformation fromH2 t o S2 will be fa vored on thermodynamic grounds.Such a transformation may be real ized through a ringsli ppage m echani sm i n w hi ch t he b ondi ng m ode ofpyrrole formally changes from 5 t o . The concept ofligand ring slippage in organ ometa llic chemistry, espe-cial ly with reference t o 5 T3 haptotropic shifts for

Figure 13. Relative G298DMol3/G G A/P W91/D NP pot en -t ia l energy surfaces for 5-pyrrole Cl and ClAlMe3 a nionmod els (kca l/mol ).

Figure 14. Relative G298DMol3/G G A/P W91/D NP pot en -t ia l energy surfaces for -pyrrole Cl and ClAlMe3 anionmod els (kca l/mol ).



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cyclopentadienyl and indenyl l igands,33 is well docu-mented. Experimental studies by Kershner a nd B asolo34

on5-heterocyclic man ga nese t ricarbonyl complexes a lsosuggest tha t pyrrole ring sl ippage is more fa cile com-pared to the isoelectronic cyclopentadienyl ligand. Re-cently, theoretical studies by Veiros 35 on pyrrolyl Mncomplexes showed that pyrrole ring slippage essentiallyoccurs between 5- and -bonding modes, w ith no loca lm i ni m um found for a 3-bonding mode. This is incontr a st to the preferred5 T3 bonding mode cha ngesobserved for cyclopenta dienyl deriva tives.

Three ar eas on t he potentia l energy surfa ce displayedin Figure 9 w ere identi fied w here ring sl ippage of thepyrrole l igand may have an impact on the calculatedenergetics, viz. , the five-membered metallacycles (H2TS2), t he seven-membered met a llacycles (H6 TS6),and the 1-hexene coordination complexes (H8 T S8).The t ra nsi t ion structures for r ing sl ippage betweenthese equilibrium structures were successfully opti-mized and are i l lustrated as R2, R 6, and R8 in Figure15 for H2TS2, H6TS6, and H8TS8, respectively.

The coordination of pyrrole in R2 resembles a dis-torted 3-bonding mode in which the Cr-C2 (2.448 )a n d C r-C5 (2.256 ) distances are not similar 36 a ndt he C r-N dist a nce (2.018 ) is elonga ted compar ed t o

the Cr-N dista nce in S2(1.873 ). As m ent ioned a bove,the metal lacycle transi t ion structure, H1-2, is ener-getical ly favored, and i t is thus assumed that H2 willbe the direct metallacycle product. Transformation ofH2 t o S2, via the ring slippage transition structureR2,is ca lculat ed to proceed with a low a ctivat ion ba rrier of2.6 kca l/mol a nd a ga in in energy of 9.1 kca l/mol, as

summarized in Table 3. This facile predicted change ofb onding m ode em phasi z es t he prob ab il it y t hat t he-pyrrole five-membered meta llacycle is a therm ody-namic sink in this area of the potential energy surface.Metallacycle growth necessarily then involves S2, a n dnot H2, a s t he di rect reagent s t ruct ure. I nsert ion ofethylene into the C r-C1 bond of S2 is calculated to bea concerted process an d proceeds with a ra th er high one-step activat ion barrier of 33.1 kcal/mol (Figure 9).Nevertheless, the lower relat ive energy of the -pyrrolemetal lacycle growth transi t ion structure, S3-4, com-p a r e d t o t h e 5-pyrrole counterpart, H3-4, suggests

t h a t t h e -coordinat ion mode dominat es in this regionof t h e P E S a n d t h a t r in g s li pp a g e p r ior or d u r in gmetallacycle growth is unlikely (Figure 9).

The relatively lower energies of S4, S5, a n d S6, a sw ell as t he m ore fav orab l e a ct i v at i on energi es forconforma tional cha nges of the seven-membered meta l-lacycles, compared to the5-an alogues suggest tha t ringsli ppage of t he pyrrol e r i ng w i ll m ost l ikel y not b eoperating in this a rea of the potential energy surfa ce.The rela tively lower energy of th e-hydrogen migrationtransi t ion structure H7-8 compared to S7-8 does,however, suggest t ha t f5 ring slippage in th e mostlikely precursor, S6, is probable. The coordination ofpyrrole in the transi t ion structure for S6 T H6 ringslippage,R6 (Figure 15), involves a distorted 3-bondingm ode s im i lar t o t he geom et ry of R2. The activat ionenergy for the sequence S6fR6 f H6 is 14.6 kcal/mol a nd is end oth erm ic by 12.0 kcal/mol (Ta ble 3). Thisa ctivation bar rier should be compa red to th e competingmechanistic sequence S6fS7-8fS8, w hich proceedswith an almost identical activation energy of 14.5 kcal/mol (Figur e 9). Conseq uent ly, no preference is found forring slippage (S6fH6) or -pyrrole-hydrogen migra-t ion on kinetic grounds. However, inspection of therelat i v e energy profi les i n Fi gure 9 rev eal s t hat t he-hydr ogen migra tion bar rier (for 5-bonded pyrr ole) isdictated by the act ivat ion barrier for formation of the

agostic intermediateH7, from which subsequent 1-hex-ene liberation essentially proceeds without barrier. Itis thus envisaged that -hydrogen migration from S6,with concomita nt ring slippage, will give preva lence toa direct mechanistic sequence S6fH7, which shouldnot only represent the lowest energy path for -hydro-gen migration fromS6but a lso provide for t he format ionof the t hermodyna mically more fa vored 1-hexene com-plex, H8. This reasoning is further supported by thesignificantly earlier nature of the transition state, H7-8, compared to S7-8 (vide supra).

The earl ier nature of H7-8, compared to S7-8, isrelated to the relat ive Cr-ligand dista nce flexibility inthe proposed mechanism. In Figure 16 the relat ive Cr-

(33) OConnor, J . M.; C asey, C. P . Chem. Rev. 1987, 87, 307.(34) Kershner, D. L .; Ba solo, F. J . Am. Chem. Soc.1987, 1 09, 7396.(35) Veiros, L . F . J. Organomet. Chem. 1999, 587, 221.(36) This dist orted 3-coordination mode of the pyrrole ligand in R 2

may also be described as a distorted 2-coordination mode in which Nand one adjacent C in the pyrrole ring are most ly involved in thebonding. This effect is more pronounced in the geometries ofR 6 a n dR8.

Figure 15. DMol3/G G A/P W91/DN P optim ized st ru ctu resof R2, R6, a n d R8.

Table 3. Calculated Activation and R eactionGibbs Free Energies (298.15 K) for Selected

Pyrrole Ring Slippage Transformations

ring slippagetransformation

Gq298(kca l/mol)

G298(kca l/mol )

H2fS2 2.6 -9.1S2fH2 11.7 9.1H6fS6 2.6 -12.0S6fH6 14.6 12.0H6fS6 10.9 5.0

S6fH6 5.9 -5.0



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pyrrole distances37 for 5- an d -bonded pyrrole, for allsta tionary points (Figures 9 and 10), ar e plotted aga instt he reac t i on c oordi nat e . I n general , i t i s found t hatw hereas t he C r--pyrrole distances show a maximumdifference of 0.035 with no significant trend along thereaction coordinate, the Cr-5-pyrrole dista nces showa maximum difference of 0.097 and a definite trend

related to the oxidation state of Cr. The Cr(II) species,H1 a nd H8, exhibi t relat ively short Cr-pyrrole dis-ta nces of 1.902 and 1.927 , wh erea s t he Cr (IV) specieshav e an a v erage C r-pyrrole distance of 1.975 . Uponfollowing the mechanistic sequence H6fH6-7fH7fH7-8fH8, an incrementa l decrea se in Cr-pyrroledistances of 1.981 f1.960 f1.914 f1.909 f1.902 is observed (Figure 16), effectively suggesting that acloser proximity of the 5-bonded ring wil l favor thereductive elimina tive -hydr ogen migra tion process. Asimilar Cr-pyrrole distance contraction is not observedduring -hydrogen migration of the -bonded pyrrolecomplexS6 t o S8. The a pparently favora ble contra ctiono f t h e 5-b on d ed p yr r ol e i n t h e f in a l s t a g e of t h e

proposed mechanism is also reflected in the relativelyearly na ture of the tra nsition structure H7-8comparedt oS7-8, in which a relat ively short C2-H distance of1.360 for t he former is observed versus 1.482 fort he l a t t er .

The 5-pyrrole 1-hexene coordination complex, H8, is5.0 kca l/mol lower in energy compar ed t o th e corre-sponding -pyrr ole complex, S8. Therefore, if the S8complex is the preferred direct 1-hexene coordina tioncomplex, ring slippage from S8 t o H8 is likely, which iscalculated to proceed w ith a n act ivat ion bar rier of 5.9kcal/mol. Tra nsform a tion of H1 from H8by substitutionof 1-hexene with 2 equiv of ethylene regenerates thefirst a ct ive intermediat e in the proposed ethylene tri-

merizat ion cycle.Population Analysis. The calculat ed Hirshfeld

charges located on Cr, the pyrrole ring, 38 an d Cl for a l lstationary points on the potential energy surface of theCl models are gra phica lly illustra ted in F igure 17. Theav erage c harges on C r and pyrrol e for t he 5-bondedpyrrole models in Figure 17 are 0.445 and -0.039 e,respectively, while the corresponding average charges

on Cr a nd pyrrole for t he -bonded pyrr ole models a re0.511 and -0.201 e, respectively. The sl ightly lessposi t ive charge on Cr and significantly less negative

charge on pyrrole, for the 5-bonded models comparedt o t he-bonded models, suggest that the charge distri-bution betw een metal a nd ligan d for the former is moredispersed compared to the lat ter. This effect is morepronounced between pyrrole and Cr for t he tw o modelst h a n f o r C r a n d C l , a s i s e v i d e n t f r o m t h e s i m i l a ravera ge Hirshfeld charges on Cl for the 5- (-0.234 e)a nd -bonded pyrrole (-0.213 e) models.

The H irshfeld char ges on C r, with the exception ofH3, H3-4, and S3-4, ar e related to the formal oxida-tion sta te of Cr. The Cr (II) complexes a t t he beginningand end of the proposed mechanism exhibit relativelysmaller positive charges on Cr compared to the Cr(IV)

complexes. This is in a greement wit h a less pronouncedelectron distribution at the Cr center for the Cr(IV)oxidation sta te compared t o the C r(II) oxidation sta te.The relative lowering in positive charge on Cr for H3,H3-4, a n d S3-4 i s qual i t a t i v el y a t t r i b ut ed t o t heintroduction of addit ional electron densi ty to the Crcenter upon incorporat ion of a t hird eth ylene fragm entto the catalytic cycle. This lowering of charge on Cr isconsistent with temporary expansion of coordinationnumber of Cr for ethylene coordination (H3) and con-certed ethylene insertion (H3-4 a nd S3-4). I t is alsoi nt erest i ng t o not e t hat a good correlat i on b et w eencharge varia tion on Cr an d distan ce between Cr and th e5-bonded pyrrole ring (see Figure 16) exists.

(37) The Cr-pyrrole distances for 5-bonded pyrrole refer to thed i s t a n c e o f t h e C r-pyrrole centroid axis, whereas the Cr-pyrroledistances for -bonded pyrrole refer to the Cr-N dista nces.

(38) The tota l Hirsh feld charge of t he pyrr ole ring is calculated bysumma tion of all Hirshfeld charges locat ed on the respective at oms inthe ring.

Figure 16. Varia t ion in Cr-pyrrole distance for 5- and-pyrrole (Cl model) along the reaction coordinate of theproposed mechanism.

Figure 17. Relat ive DMol3/G G A/P W91/D NP ca lcul a t edH ir s h feld ch a r ges o n C r , p y r role, a n d C l f or 5- a n d-pyrr ole (Cl model).



16/16

Conclusions

In this theoretical contribution on Cr-cat alyzed t ri-merizat ion of ethylene a mechanism is proposed for theP hillips (Cr-pyrrolyl) trimeriza tion cat a lyst syst em an denergies for the di fferent steps are calculated at thenonlocal DF T (DMol3/G G A/P W91/D NP ) level of t he ory .A detai led an alysis t o determine the preferred groundspin sta te for the a ctive Cr(II) an d Cr (IV) species in themechanism was conducted. From these calculations it

w as det erm i ned t hat t he t r i pl et spi n s t a t es for b ot hCr(II) an d C r(IV) ar e predicted t o be the ground st at eat t he GG A/P W91 l evel of t heory . Bot h addi t i onalpossible spin states for the Cr(II) species (singlet andqui nt et ) , as w el l as t he s i ngl et spi n s t a t e for C r( I V )species, were found to be significantly more unfavorablebased on relative electronic energies. The main conclu-si on from t hese resul t s w as t hat spi n s t a t e c rossi ngduring the proposed mechanism is unlikely to occur,effectively eliminating the necessity to locat e minimumenergy crossing points (MECPs) for the proposed mech-anism. The proposed ethylene trimerization mechanismis based on t he format ion of meta llacycle intermediat es.Two important features of the proposed mechanismwere explicitly investiga ted: first, the preferred coor-dination mode of the pyrrole ligand in each step of themechan ism, a nd second, the importa nce of expan sionof a model Cl anion to a more realistic ClAlMe3 a nionfragment.

The calculated Gibbs free energy profiles at 298.15K (Cl model) for the full potential energy surfa ces of5- a n d a -coordinated pyrrole were both found to befavorable on thermodynamic grounds, with Goverall )-20. 9 and -17.1 kcal/mol, respectively. The ra te-determining step in the mechanism for both bondingm odes of pyrrol e w as m et al l ac yc l e grow t h from t hecorresponding metalla cyclopentan e reagent to the met-alla cyclohepta ne product w ith Gqoverall ) 38.2 a nd 33.1kca l/mol for 5- and -bonded pyrr ole, respectively. Weha ve shown t ha t th e cha nge of pyrrole bonding mode isan importa nt concept in t he proposed mechanism. A 5-

bonding mode of pyrrole is calculat ed to be fa vored formetal lacycle formation, whereas a -bonding mode isfavored for metallacycle growth and changes in confor-mations of seven-membered metallacycle intermediates.No preference wa s found for5- or -pyrrole in the finalreductive el imina tive l iberat ion of 1-hexene in theproposed mechan ism. Tra nsition sta te geometries werecalcula ted for pyrr ole ring slippage (5 T) for selectedsta tionary points on the potentia l energy surface, which

showed that the act ivat ion barrier for bonding modechang e is small. These theoretica l results th us suggestthat facile change of pyrrole bonding mode enhances thecatalytic efficiency of the Cr-pyrrolyl ethylene trimer-ization.

P ot ent i a l energy surfac e c al c ul at i ons on t he m orerea listic ClAlMe3 ani on m odels show ed rem arkab lesimilarities to the PES obtained for the stripped-downCl models. One importa nt di fference for calculatedactivat ion energy for metallacycle growth w as, h owever,found for th e-coordinated pyrrole models. A significantlowering of act ivat ion energy of the rat e-determiningstep by 11.3 kcal/mol is found for the ClAlMe3 modelcompared to the stripped-down Cl model in this step.

This result suggests tha t t he ful l aluminat e anion mayhave an important role in control ling the reactivity ofthe C r-pyrrolyl cata lyst system.

Acknowledgment. We a c kn ow l ed g e M r . I v a nBester (Information Management, Sasol)for the efficientw ay i n w hi c h he m anages a l l t ec hni c al sof t w are andhardw a re requirem ent s of t he Mol ecul ar Modeli ngdepart ment a t S asol Technology. We also wish t o tha nkthe members of the Sasol ethylene trimerization groupfor frui t ful discussions and Sasol Technology Ltd forpermission to publish this work.

Supporting Information Available: Cartesian coordi-

na tes for all optimized geometries. This informat ion is ava il-a ble free of char ge via t he Int ernet a t h tt p://pubs.a cs.org.

OM0306269


a dft study toward the mechanism of

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